diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index 52d194d..a14c3fb 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -44,7 +44,7 @@
    "source": [
     "import graphviz\n",
     "import sympy as sp\n",
-    "from sympy import re, im, I, E, symbols, Sum"
+    "from sympy import re, im, I, E, symbols, Sum, IndexedBase, Function"
    ]
   },
   {
@@ -127,6 +127,48 @@
     "tags": []
    },
    "outputs": [],
+   "source": [
+    "s, m_a2, Gamma_a2 = symbols(\"s m_a2 Gamma_a2\")\n",
+    "a_m = IndexedBase(\"a_m\")\n",
+    "Y2_m = Function(\"Y_2^m\")(\"Omega_1\")\n",
+    "m = symbols(\"m\", cls=sp.Idx)\n",
+    "\n",
+    "A12 = sp.Sum(a_m * Y2_m, (m, -2, 2)) / (s - m_a2**2 + I * m_a2 * Gamma_a2)\n",
+    "A12"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "m_Delta, Gamma_Delta = symbols(\"m_Delta Gamma_Delta\")\n",
+    "b_m = IndexedBase(\"b_m\")\n",
+    "Y1_m = Function(\"Y_1^m\")(\"Omega_2\")\n",
+    "A23 = Sum(b_m * Y1_m, (m, -1, 1)) / (s - m_Delta**2 + I * m_Delta * Gamma_Delta)\n",
+    "A23"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "c0, m_Nstar, Gamma_Nstar = symbols(\"c_0 m_N* Gamma_N*\")\n",
+    "A31 = c0 / (s - m_Nstar**2 + I * m_Nstar * Gamma_Nstar)\n",
+    "A31"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],